Expected utility for nonstochastic risk

Ivanenko, Victor and Pasichnichenko, Illia (2016): Expected utility for nonstochastic risk.

Abstract

The world of random phenomena exceeds the domain of the classical probability theory. In the general case the description of randomness requires a specific set of probability distributions (which is called statistical regularity) rather than a singe distribution. Such statistical regularity arises as a limit of relative frequencies. This approach to randomness allows to generalize the expected utility theory in order to cover the decision problems under nonstochastic random events. Applying the von Neumann-Morgenstern utility theorem, we derive the maxmin expected utility representation for statistical regularities. The derivation is based on the axiom of the preference for stochastic risk, i.e. the decision maker wishes to reduce the set of probability distributions to a single one.

• Item Type: MPRA Paper
• Language: English
• Keywords: expected utility, risk, mass phenomena, statistical regularity, nonstochastic randomness, multiple prior
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

References

Borel, E., 1956. Probabilite et certitude. Presses universitaires de France, Paris.

Chateauneuf, A., Faro, J.H., 2009. Ambiguity through confidence functions. Journal of Mathematical Economics 45, 535-558.

Chian, A.C.L., Rempel, E.L., Rogers, C., 2006. Complex economic dynamics:Chaotic saddle, crisis and intermittency. Chaos, Solitons & Fractals 29, 1194-1218.

Dubois, D., Prade, H., 1989. Fuzzy sets, probability and measurement. European Journal of Operational Research 40, 135-154.

Fishburn, P.C., 1982. The Foundations of Expected Utility. Springer Netherlands, Dordrecht.

Gilboa, I., Schmeidler, D., 1989. Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18, 141-153.

Herstein, I., Milnor, J., 1953. An axiomatic approach to measurable utility. Econometrica 21, 291-297.

Ivanenko, V., Labkovsky, V., 1986. On the functional dependence between the available information and the chosen optimality principle. Lecture Notes in Control and Information Sciences 81, 388-392.

Ivanenko, V.I., 2010. Decision Systems and Nonstochastic Randomness. Springer, New York.

Ivanenko, V.I., Labkovsky, V.A., 2015. On regularities of mass phenomena. Sankhya A 77, 237-248.

Ivanenko, Y., Pasichnichenko, I., 2014. On one definition of uncertainty. Risk and Decision Analysis 5, 139-148.

Jaffray, J., 1989. Linear utility theory for belief functions. Operation Research Letters 8, 107-112.

Kolmogorov, A., 1986. On the logical foundations of the probability theory [in Russian], in: Probability Theory and Mathematical Statistics. Nauka, Moscow, pp. 467-471.

Lux, T., 1998. The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions. Journal of Economic Behavior & Organization 33, 143-165.

Miller, J.I., Ratti, R.A., 2009. Crude oil and stock markets: Stability, instability, and bubbles. Energy Economics 31, 559-568.

von Neumann, J., Morgenstern, O., 1947. Theory of Games and Economic Behavior, 2nd edition. Princeton University Press, Princeton.

Pasichnichenko, I.O., 2016. On the axiomatic definition of generalized maximin principle. Cybernetics and Systems Analysis 52, 312-318.

Zorich, I., Ivanenko, V., Munier, B., 2000. On the construction of the regularity of statistically unstable system. Journal of Automation and Information Sciences 32, 84-87.